If a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40 . Mathematics and Physics 30 , Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18 . The number of students who have opted Mathematics alone is

Step-by-step solution

Let M, P and C be the set of students who opted Mathematics, Physics and Chemistry respectively. Then, n(M)=100, n(P)=70, n(C)=40n(M P)=30, n(M C)=28, n(P C)=23 , n(M P C)=18 Number of students who opted Mathematics alone aligned &=n (M P^ C^ ) &=n (M (P C)^ ) &=n(M)-n(M (P C)) &=n(M)-n((M P) (M C)) &=n(M)-n(M P)-n(M C)+n(M P C) &=100-30-28+18=60 aligned